The second generalized Hamming weight of some evaluation codes arising from a projective torus

In this paper we give a formula for the second generalized Hamming weight of certain evaluation codes arising from a projective torus. This allows us to compute the corresponding weights of the codes parameterized by the edges of a complete bipartite graph. We determine some of the generalized Hamming weights of non-degenerate evaluation codes arising from a complete intersection in terms of the minimum distance, the degree and the a-invariant. It is shown that the generalized Hamming weights and the minimum distance have some similar behavior for parameterized codes These results are used to find the complete weight hierarchy of some codes.